Reconstructing discrete measures from projections. Consequences on the empirical Sliced Wasserstein Distance

Eloi Tanguy, Rémi Flamary, Julie Delon

This paper deals with the reconstruction of a discrete measure ${\gamma }_Z$ on ${\mathbb{R}}^d$ from the knowledge of its pushforward measures $P_i\#{\gamma }_Z$ by linear applications $P_i: \mathb…